Team Toad: Motor Mathematics

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Message 2672.5 Electrical power for DC motors

Oct-16 6:35 pm

1. Ohms law, electricity

V=IR (volts = current times resistance)
P=IV (power = current times volts), watts.
745 watts = 1 horsepower

2. Dynamics

1 pound applied to a one foot lever is one foot-pound, = 12 inch-pounds.
Power = torque times rpm.
1 horsepower = 550 foot-pounds per minute.

Using speed reducers (gear/belt/chain), the rpm is divided by the ratio, and the torque is multiplied. (minus a little loss)
Take the torque at the axle, and divide by the radius of the wheel (watch units) - that will give you pushing force at the wheel.
Traction at wheel = weight on wheel times coeffecient of friction. A good rubber wheel will have a coefficient of about 0.9
Use commonsense and apply the two rules above (i.e. a 50 pound bot with 100 pounds of push = spinning wheels)

3. DC Motors.

A permanent magnet dc motor (PMDC) is most common.
They produce maximum torque at zero speed; this is called stall torque.
They produce not too much torque at maximum speed.
They produce maximum power at 1/2 speed.
At best, they only turn 50% of the electrical power into motive power.

One specification often given is no load current (i.e. 4 amps at 2500 rpm). That is almost useless. The specification you need is stall current; how much the motor draws with the shaft held from turning (same condition as stall torque, also same condition as trying to shove another robot). That value is 6 to 20 times the no load current. THAT is what you should use to size your motor controller; you can use the 'transient' rating.

Message 2672.6

Oct-16 6:46 pm

At best, they only turn 50% of the electrical power into motive power.

Although the rest of your list was excellent, this part is only true for cheap motors (Jensens, starters, ect) that aren't built for continous use. The precision industrial servomotors I used in Spike were rated at >80% efficient at max power out. Of course, the design of your robot's drivetrain and where in its torque curve the motor will spend it's time operating make a big difference - a stalled motor is running at 0% efficiency.

-Andrew Lindsey

Message 2164.3 Wheel size, Torque, Speed & Force

Oct-1 11:37 pm

Here are the formulas you need:

Circumference of wheel = diameter x 3.14 /12 (inches per foot)
RPM x circumference (feet) = robot speed, feet per minute.
Speed, feet per minute / 60 = speed, feet per second    missing step added by Fuzzy
Speed, feet per second x 0.682 = speed, miles per hour
Example: 6"wheel, 100 rpm = 2.6 feet per second, 1.8 mph [too slow]

Motor torque, ft-lbs x diameter/2 x 1/12 (inches pre foot) = pounds of pushing force, per wheel. (assumes one wheel per motor, and that you have traction...)
Traction = Weight on wheel x friction factor.
Friction factor is 0.5 to 0.9 for REALLY sticky wheels.

Example: 20 in-lbs final torque, 6" wheels = 60 pounds force.. in a 50 pound robot? unless you are carrying your opponent, you'll just spin your wheels.

One more.. Force = Mass x acceleration
(best done by example)
If your bot musters 30 pounds pushing force, and weighs 55 lb, Well, to get the units right I do it this way:
It will accelerate at 30/55 of a 'G' which is 32 ft/sec/sec
Multiplying that out, it will go from 0 to 17.5 ft/sec in a second.

I like using an excell spreadsheet to try motors, gear ratios and wheel sizes and see how they fit.

Get the drill motor.

Edited 10/1/00 11:55:52 PM ET by KIRWAN9

Edited 2/18/02 by LAZYTOAD, error caught by  

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